Bathini Sidda Reddya*,  Jyothula Suresh Kumarb,  Chevireddy Eswara Reddyc and Kondakkagari Vijaya Kumar Reddyb

aSchool of Mechanical Engineering, RGMCET, Nandyal, Kurnool (Dt), A.P, India
bDepartment of Mechanical Engineering, J.N.T.U.H. College of Engineering, J.N, India
cDirector, The School of Engineering & Technology, SPMVV, Women’s University, Tirupati, Chittoor (Dt) A.P, India

 

Download Citation: |
Download PDF


ABSTRACT

The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT). This study considers the thickness stretching effect and non-zero transverse shear stresses conditions on the top and bottom surfaces of the plate. It does not require shear correction factors. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The equations of equilibrium and boundary conditions are derived using the principle of virtual work. Solutions are obtained for FGPs in closed-form using Navier’s technique. Comparison studies are performed to verify the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the buckling behavior of functionally graded plates. The effect of side-to-thickness ratio, aspect ratio, modulus ratio, the volume fraction exponent and the loading conditions on the critical buckling load of FGPs is also investigated and discussed.


Keywords: Functionally graded plates; thickness stretching effect; higher order shear deformation theory; Navier’s method closed form solutions; buckling analysis.


Share this article with your colleagues

 


REFERENCES

  1. [1] Javaheri, R. and Eslami, M. R. 2002. Buckling of functionally graded plates under in-plane compressive loading. Journal of Applied Mathematics and Mechanics, 82, 4: 277-283.

  2. [2] Abrate, S. Functionally graded plates behave like homogeneous plates. Composites part B, 38, 1: 151-158.

  3. [3] Mohammadi, M., Saidi, A.R., and Jomehzadeh, E. 2010. Levy solution for buckling analysis of functionally graded rectangular plates. Applied Composite Materials, 17, 2: 81-93.

  4. [4] Mahdavian, M. 2009. Buckling analysis of simply supported functionally graded rectangular plates nunder non-uniform in-plane compressive loading. Journal of Solid Mechanics, 1, 3: 213-225.

  5. [5] Feldman, E. and Aboudi, J. 1997. Buckling analysis of functionally graded plates subjected to uniaxial loading. Composite Structures, 38, 1-4: 29-36.

  6. [6] Samsam Shariat, B. , Javaheri, R., and Eslami, M. R. 2005. Buckling of imperfect functionally graded plates under in-plane compressive loading. Thin-Walled Structures, 43, 7:1020-1036.

  7. [7] Tung, H. V. and Duc, N. D. Nonlinear analysis of stability for functionally gradedplates under mechanical and thermal loads. Composite Structures, 92, 5:1184-1191.

  8. [8] Reissner, E. 1945. The effect of transverse shear deformation on the bending of elastic plates. ASME Journal of Applied Mechanics, 12, 2: 69-77.

  9. [9] Mindlin, R. 1951. Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. ASME Journal of Applied Mechanics, 18: 31-38.

  10. [10] Thai, T. and Vo, T. P. 2013. A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Applied mathematical modelling, 37: 3269-3281.

  11. [11] Yang, J., Liew, K.M., and Kitipornchai, S. 2005. Second-order statistics of the elastic buckling of functionally graded rectangular plates. Composites Science and Technology, 65, 7–8: 1165-1175.

  12. [12] Mohammadi, M., Saidi, A. R., and Jomehzadeh, 2009. A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges”, Proceedings of IMechE Part C: Journal of Mechanical Engineering Science, 224: 1831-1841.

  13. [13] Zhao, X., Lee, Y. Y., and Liew, K. 2009. Mechanical and thermal buckling analysis of functionally graded plates. Composite Structures, 90, 2: 161-171.

  14. [14] Sepiani, H. A., Rastgoo, A., Ebrahimi, F., and Ghorbanpour Arani, A. 2010. Vibration and buckling analysis of two-layered functionally graded cylindrical shell, considering the effects of transverse shear and rotary inertia. Materials & Design, 31, 3: 1063-1069.

  15. [15] Naderi, A. and Saidi, A 2010. On pre-buckling configuration of functionally graded Mindlin rectangular plates. Mechanics Research Communications, 37, 6: 535-538.

  16. [16] Saha, and Maiti. P.R. 2012. Buckling of simply supported FGM plates under uniaxial load. International Journal of Civil and Structural Engineering, 2, 4:1036-1050.

  17. [17] Javaheri, R. and Eslami, Mr. 2002. Thermal buckling of functionally graded plates based on higher order shear deformation theory. Journal of Thermal stresses, 25, 7: 603-625.

  18. [18] Najafizadeh, M. and Heydari, H. R. 2004. Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory.European Journal of Mechanics - A/Solids, 23, 6: 1085-1100.

  19. [19] Bodaghi, M. and Saidi, A. 2010. Levy-type solution for buckling analysis of thickfunctionally graded rectangular plates based on the higher-order shear deformation plate theory. Applied Mathematical Modelling, 34, 11: 3659-3673.

  20. [20] Bagherizadeh, , Kiani, Y., and Eslami, M. R. 2011. Mechanical buckling of functionally graded materialcylindrical shells surrounded by Pasternak elastic foundation. Composite Structures, 93, 11: 3063-3071.

  21. [21] Mozafari, and Ayob, A. 2012. Effect of Thickness Variation on the Mechanical Buckling Load in Plates Made of Functionally Graded Materials. Procedia Technology, 1:496-504.

  22. [22] Ma, L. S, and Wang, T. J. 2003. Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings. International Journal of Solids and Structures, 40, 1-14: 3311-3330.

  23. [23] Hosseini-Hashemi, , Khorshidi, K., and Amabili, M. 2008. Exact solution for linear buckling of rectangular Mindlin plates. Journal of Sound and Vibration, 315: 318-342.

  24. [24] Saidi, A.R., Rasouli, A, and Sahraee, S. 2009. Axisymmetric bending and buckling analysis of thickfunctionally graded circular plates using unconstrained third-order shear deformation plate theory. Composite Structures, 89, 1: 110-119.

  25. [25] Oyekoya, O. O. Mba, D. U., and El-Zafrany, A.M. 2009. Buckling and vibration analysis of functionally graded composite structures using the finite element method. Composite Structures, 89, 1: 134- 142.

  26. [26] Ghannadpour, S. A. M., Ovesy, H. R., and Nassirnia, M. 2012. Buckling analysis of functionally graded plates under thermal loadings using the finite strip method. Computers & Structures, 108—109: 93-99.

  27. [27] Thai, T. and Choi, D. H. 2012. An efficient and simple refined theory for buckling analysis of functionally graded plates. Applied Mathematical Modelling, 36: 1008-1022.

  28. [28] Uymaz, and Aydogdu, M. 2013. Three dimensional mechanical buckling of FG plates with general boundary conditions. Composite Structures, 96: 174-193.

  29. [29] Lal, A., Jagtap, K.R., and Singh, B.N. 2013. Post buckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties. Applied Mathematical Modelling, 37, 5-1: 2900-2920.


ARTICLE INFORMATION

Received: 2013-09-03
Revised: 2014-10-09
Accepted: 2014-11-20
Available Online: 2015-03-01


Cite this article:

Reddy, B.S., Kumar, J.S., Reddy, C.E., Reddy, K.V.K. 2015. Buckling analysis of functionally graded plates using higher order shear deformation theory with thickness stretching effect. International Journal of Applied Science and Engineering, 13, 19–35. https://doi.org/10.6703/IJASE.2015.13(1).19

Other people also read ...